How do I handle a dog biting me?

I'm five days into a seven-day stay with a dog (first time caring for this particular pup). When we did the meet-and-greet, the owner told me he's a rescue and that he can get snarly when he's first meeting people, particularly when they get up in his face. The dog and I have built up a good rapport the last few days and have had some good snuggle time on the couch, so I thought he had gotten over the initial jitters. Clearly I miscalculated, because last night I was leaning in to pet him, and evidently got too close (or maybe was just coming at him from a weird angle), because suddenly he freaked out, snarled, and bit me in the face.

I'm mostly fine, but I have a couple of puncture wounds around my nose and cheek, as well as a puffy black eye. I got a tetanus shot just in case, and I'm not sure about the dog's rabies vaccination. Is this something I need to report to Rover? Also, any advice on what to say to the owner about it? He really is a very sweet dog, and I feel like it was largely my fault that this happened, since the owner did kind of warn me (although she didn't mention anything about a history of biting, so I don't know if this was the first time he's done that or not), but I'm going to have some medical bills, and I'm not sure if that's something I should be involving anyone else in or not.

Thanks!